Testing noninferiority in three‐armed clinical trials based on likelihood ratio statistics

Clinical noninferiority trials with at least three groups have received much attention recently, perhaps due to the fact that regulatory agencies often require that a placebo group be evaluated along with a new experimental drug and an active control. The authors discuss likelihood ratio tests for binary endpoints and various noninferiority hypotheses. They find that, depending on the particular hypothesis, the test reduces asymptotically either to the intersection‐union test or to a test which follows asymptotically a mixture of generalized chi‐squared distributions. They investigate the performance of this asymptotic test and provide an exact modification. They show that this test considerably outperforms multiple testing methods such as the Bonferroni adjustment with respect to power. They illustrate their methods with a cancer study to compare antiemetic agents. Finally, they discuss the extension of the results to other settings, such as Gaussian endpoints.     

An analysis of participation factors and effects of the active labour market measure Graduate practice in Slovakia – Counterfactual approach

The paper presents the results of the evaluation of the selected active labour market policy measure “Contribution to the Graduate practice” in Slovakia. The measure is of a voluntary nature and its main aim is to prevent long-term unemployment among young people and to support a competitive ability of young school-leavers and thus their employability and sustainability in the labour market through the acquisition of work experience, professional skills and work habits. In the study, we analyse the selected characteristics of young jobseekers who participated in this measure in 2016 and their counterfactuals who did not participate. In addition to 2016, the observed period includes a subsequent 2 years – the individual impact period of the measure for each participant, i.e. the years 2017 and 2018. We evaluated the effects of the measure by applying the exact matching of treated and non-treated individuals using the outcome variables, namely wages and placement in the labour market in the impact period of the measure. The results indicate that the Graduate practice had a positive impact on the employability and sustainability of its participants, but rather in short-term or maximum long-term. Regarding the wage levels referring to the financial appraisal of the participants of the measure, the results suggest that non-treated individuals were better financially evaluated and so the Graduate practice did not guarantee better salary to its participants. The findings of the study are important in the setting of conditions of the measure for future periods in order to achieve its better functioning and efficiency in the way of proper targeting, more efficient use of funds, and for a system of their redistribution.     

Hilbert空间中框架的几个性质

本文研究了Hilbert空间中框架的几个性质,并订正了文献1中的一个错误结论。     

Calibrated linear unbiased estimators in finite population sampling

Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38] and Rao [2002. Discussion of “Exact linear unbiased estimation in survey sampling”. J. Stat. Plann. Inf. 102, 39–40] suggested some useful techniques of deriving a linear unbiased estimator of a finite population total by modifying a given linear estimator. In this paper we suggest various generalizations of their results. In particular, we search for estimators satisfying the calibration property with respect to a related auxiliary variable and obtain some new calibrated unbiased ratio-type estimators for arbitrary sampling designs. We also explore a few properties of one of the estimators suggested in Sugden and Smith [2002. Exact linear unbiased estimation in survey sampling. J. Stat. Plann. Inf. 102, 25–38].     

Bayesian estimation for time-series regressions improved with exact likelihoods

We propose an estimation procedure for time-series regression models under the Bayesian inference framework. With the exact method of Wise [Wise, J. (1955). The autocorrelation function and spectral density function. Biometrika, 42, 151–159], an exact likelihood function can be obtained instead of the likelihood conditional on initial observations. The constraints on the parameter space arising from the stationarity conditions are handled by a reparametrization, which was not taken into consideration by Chib [Chib, S. (1993). Bayes regression with autoregressive errors: A Gibbs sampling approach. J. Econometrics, 58, 275–294] or Chib and Greenberg [Chib, S. and Greenberg, E. (1994). Bayes inference in regression model with ARMA(p, q) errors. J. Econometrics, 64, 183–206]. Simulation studies show that our method leads to better inferential results than their results.     

Exact Inference for a Population Proportion Based on a Ranked Set Sample

ABSTRACT

This article develops and investigates a confidence interval and hypothesis testing procedure for a population proportion based on a ranked set sample (RSS). The inference is exact, in the sense that it is based on the exact distribution of the total number of successes observed in the RSS. Furthermore, this distribution can be readily computed with the well-known and freely available R statistical software package. A data example that illustrates the methodology is presented. In addition, the properties of the inference procedures are compared with their simple random sample (SRS) counterparts. In regards to expected lengths of confidence intervals and the power of tests, the RSS inference procedures are superior to the SRS methods.     

On certain unbiased product estimators

When data on an auxiliary variate is available on all the units of the population, negatively correlated with the study variate, Robson (1957) and Murthy (1964) proposed product method of estimation for the estimation of the population total (mean) of the study variate. In this paper, we discuss a method given in Rao (1983) and obtain a simpler dervation of the class of unbiased product estimators for the case of Simple Random Sampling WithOut Replacement design as well as for the case of interpenetrating subsamples design which follows as a limiting case. Finally, we shall illustrate the results by means of two simple numerical example from live data.     

The unbiasedness of hodges and lehman's test for a composite hypothesis of the man of a distribution with unknown variance

In 1954 Hodges and Lehmann considered the following problem: given is an i.i. normally distributed random sample with variance unknown. Under the null-hypothesis the mean is contained in a prescribed interval. Hodges and Lehmann constructed a test similar on the interval. This test is superior in power to the usual auxiliary procedure applied to this problem. Numerical calculations by Hodges and Lehmann indicated that the test is unbaised, however an analytical proof could not be given. In a recent paper the author proved unbiasedness for levels not too large, the magnitude depending on the sample size. Here the Proof is completed by establishing unbiasedness for all levels.     

The split sample permutation t-tests

Without the exchangeability assumption, permutation tests for comparing two population means do not provide exact control of the probability of making a Type I error. Another drawback of permutation tests is that it cannot be used to test hypothesis about one population. In this paper, we propose a new type of permutation tests for testing the difference between two population means: the split sample permutation t-tests. We show that the split sample permutation t-tests do not require the exchangeability assumption, are asymptotically exact and can be easily extended to testing hypothesis about one population. Extensive simulations were carried out to evaluate the performance of two specific split sample permutation t-tests: the split in the middle permutation t-test and the split in the end permutation t-test. The simulation results show that the split in the middle permutation t-test has comparable performance to the permutation test if the population distributions are symmetric and satisfy the exchangeability assumption. Otherwise, the split in the end permutation t-test has significantly more accurate control of level of significance than the split in the middle permutation t-test and other existing permutation tests.     

线性GMDH参数模型的无偏估计研究

 多元线性回归分析中,参数无偏性是参数估计方法的一个重要指标。本文对线性GMDH参数模型建立多元线性模型进行了研究,得到以下结论：一,在满足经典线性回归模型的假设条件下,其参数估计量具有无偏的性质;二,在满足其它假设条件下,可以在样本量少于待估参数的情况下建模,估计的参数也是无偏的;三,用参数GMHD方法建模时,它对完全多重共线性是免疫的。